Question

Let ƒ and g be differentiable functions satisfying g′(1) = 2, g(1) = b and ƒog = I (identity function). Then, ƒ′(2) is equal to–

• A. 2
• B. 2/3
• C. ½
• D. None of these

Answer 1

Answer: (C)

½

Answer 2

We have, ƒog = I

⇒ ƒ{g(x)} = x, for all x ∈ R

∴ ƒ′ {g(x)} . g′(x) = 1, for all x ∈ R

⇒ ƒ′(g(1)) =

⇒ ƒ′(2) = $\frac { 1 } { 2 }$

Hence, (3) is the correct answer.